We develop an efficient machine learning protocol to predict the noise-induced coherence from the nonequilibrium fluctuations of photon exchange statistics in a quantum heat engine. The engine is a four-level quantum system coupled to a unimodal quantum cavity. The nonequilibrium fluctuations correspond to the work done during the photon exchange process between the four-level system and the cavity mode. We specifically evaluate the mean, variance, skewness, and kurtosis for a range of engine parameters using a full counting statistical approach combined with a quantum master equation technique. We use these numerically evaluated cumulants as input data to successfully predict the hot bath induced coherence. A supervised machine learning technique based on K-Nearest Neighbor(KNN) is found to work better than a variety of learning models that we tested.